Multi-scale interactions in an idealized Walker cell: analysis with isentropic

We propose a new approach for analyzing multi-scale properties of the atmospheric flow that employs the recently introduced isentropic streamfunction and relies on its scale decomposition with Haar wavelets. We applied this method to a cloud resolving simulation of a planetary Walker Cell characterized by pronounced multi-scale flow. The resulting set of isentropic streamfunctions – obtained at the convective, mesoscale, synoptic, and planetary scales – captured many important features of the Walker Circulation. The convective scale was associated with the shallow, congestus, and deep clouds, which jointly dominate the upward mass flux in the lower troposphere. The synoptic and planetary scales played important roles in extending mass transport to the upper troposphere where the corresponding streamfunctions mainly captured the first baroclinic mode associated with large-scale overturning circulation. The intermediate scale features of the flow, such as anvil clouds associated with organized convective systems, were extracted with the mesoscale and synoptic scale isentropic streamfunctions. Multi-scale isentropic streamfunctions were also used to extract salient mechanisms that underlie the low-frequency variability of Walker Cell. In particular, the lag of a few days of the planetary behind the convective scale indicated the importance of the convective scale in moistening the atmosphere and strengthening the planetary-scale overturning circulation. Furthermore, the mesoscale and synoptic lags behind the planetary scale reflected the strong dependence of convective organization on shear. 14